Directional antenna array



June 9, 1931. J. s. STONE DIRECTIONAL ANTENNA ARRAY Original Filed Jan. 26, 1927 4 Sheets-Sheet l noovnoo m w 5 8 w n W N H I I T w M 7 H W v V w T 4 a a m A M wmdo J a a Y B 0 O B M 44 o F "W wa /65432 W4 23 m H \wwwhfiwu w W, 3 0 0M...

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DIRECTIONAL ANTENNA ARRAY Original Filed Jan. 26, 1927 4 Sheets-Sheet 2 ATTORN EY June 9, 1931. J. a. STONE DIRECTIONAL ANTENNA ARRAY Original Filed Jan. 26, 1927 4 Sheets-Sheet 3 is a o a auoooauooaaoouoen INVENTOR J6 fin Jaw/w Jjtone ATTORNEY June 9, 1931. J. 5. STONE 1.8089359 DIRECTIONAL ANTENNA ARRAY Original Filed Jan. 26. 1927 4 sneets-shet 4 INVENTOR Jiim Stone Stone ATTORN EY 0 a 4. 2 0 1. w w 0 w u m w w w m 5 o a w I v 0/ I I m Z .0 fa 0 .0 e v 5 4 W 4 W P 1 4 w P w i A H $256 Z a 0 A. q 1 3 0 lfia olwm J n m M... 2 JM lAx C :0 m .0 \m 1 f I EmwQ m 5& a l NMQQNQ M@.QI2I W 0 W M M \w g M w w M M a, Q5 5 z W I W m 0 Original application filed January 26, 1927,8eria1 Patented .lune 9, 1931" Uni starts Joan stone stro vn, on SAN; DIEGO, cAn'rr-onnm, essreivoa T0 AMERICAN Tntnrnonn 1 .ANI) TELEGRAPH COMPANY, A CORPORATION OF new YORK DEREGTIONAL ANTENNA ARRAY 'This invention relates to directive antenna arrays. I

The earliest means employed to direct electromagnetic waves in an approximately parallel beam was the actual cylindrical parabolic reflector. A cylindrical parabolic reflector of, for example, sheet metal, having the oscillatorsubstantially coincident with its focal line, directs rays to a conjugate cylindrical sheet metal parabolic reflector, in the focal line of which may be placed what is known as the resonator. Since the employment of this very early means of directional transmission, a number of modifications of this means have been made for securing fur,- ther directive radio communication.

In considering the use of parabolic refiectors in radio or high frequency electrical transmission, the temptation is very strong to make inappropriate and illegitimate use of'the analogue with the parabolic mirror in I its use for producing a parallel beam of light. The analogue of the parabolic mirror is safe enough if it is remembered that the light must be monochromatic, i. e., light of a single wave length, and that the dimensions of the mirror must at most be but a few wave lengt is in width. When these limitations are borne in mind, much of the utility of the light analogue as a means of clarification vanishes. In order to better understand this invention, the maximum legitimate use of the analogy with the light problem will be made in order to better understand the electromagnetic problem of short wave 0 high frequency transmission. f 'This is a division of a copending application, Serial Number 163,774, filed January 26, 1927. While this invention will be pointed out with particularity in the appended claims,

No.163,774. Divided and this application filed novemter Serial No. 409,402. i

sent curves characteristic of the invention employed as aids to an analysis and understanding of the invention. Figs. 22 and 23 represent uniform linear arrays.

Referring to Fig; 1 of the drawings, there is shown a cross-section of a cylindrical para-' bolic mirror designated by the reference characters BOO. The reference character F designates the section of an-incandescent filament whose axis lies in the focal line of the mirror. This figure shows that the light emanating from the organization consists of a parallel beam of light reflected from the mirror, and another and di vergentb'eam of primary light emanating directly from the filament which is at the focal line of the mirror. This figure also shows that the primary light from the filament which escapes from the mirror is wasted, besides being detrimental so far as thedirective effects of the system are con cerned, and clearly suggests that .an improvement could be efi'ected in the organization if this primary light could be, substantially suppressed without at the same time suppressing, orotherwise interfering with, the parallel beam oflight reflected from the parabolic mirror. This can only be done in the imagination, at least, by dispensing with the incandescent filament. and 'making the surface of the reflector at every point selfluminous in just the phasefland degree of illlumination'to which the filament formerly illuminated it. I

The degree to which the filament at the focal line of the mirror illuminates the different parts of a parabolic surface is illustrated in Fig. 2. In this figure, radial lines extend from the focus to the surface of the parabola at equal. intervals of 10 degrees,

and the spaces between them therefore represent substantially equal pencils of light emanating from the filament. The parabolic mirror is, for convenience, assumed to be a perfect reflector, and pencils of light are all reflected parallel to the axis of the parabola corresponding to those pencils of light originating at the filament and striking the surface of the parabola readily. v An inspectionof Fig. 2 shows that the surface of the parabolic mirror is illuminated most intensely at and near the vertex, and that the intensity gradually diminishes with a departure from that point outwardly along the curve. Similarly, this figure shows the varying intensity of the parallel reflected beam. The intensity of this beam is seen to be greatest at the center, and to wane gradually from that point to the periphery of the beam.

The geometry of the system is derived from Fig. 3 of the drawing showing another crossseetional view of aparabolic surface. In a parabolic curve having the equation y =taw, m 1-a and 1 being the radial distance of any point on the parabola from the focus and 6 being the angle between the radial line from the focus to the point on the parabola and the axis of the parabola Clearly, the intensity of the light of theparallel beam reflected from the mirror is proportional to The lag in the phase of the light which falls on the surface of the parabolic mirror behind that of the light emanating from the focus is given by the following expression:

cos g (2) In this expression, A represents the wave length. It will also be readily understood that the intensity of light falling upon any surface is given by in which .9 is the length of arc and 7" is the radius vector. From this it follows that 6 (10 cos a (3) a and that Viewed from a great distance, the image of the filament at the focus appears to be a cont nuously illuminated surface lying in the plane of the directrix ZZ of the parabola BOC of Figs. 2 and This plane, however, is not uniformly illuminatechthe intensity of illumination being greatest at A (directly opposite the focus) and gradually diminishing with the departure from A toward the boundaries Z and Z. Fig. 2 illustrates this variation of intensity qualitatively by the relative crowding together of the dotted vertical lines near the center of the directrix A, while the variation in intensity is illustrated quantitatively in Fi 4 of the drawings.

v Just as a parallel beam may, in the imagination, be reproduced without the intervention of the primary source at the focus by making the reflector, itself, independently luminous at every point in the degree and phase to which it would be illuminated at that point by the primary source at the focus, so this parallel reflected beam may also be reproduced without the intervention of either the source at the focus or the independently luminous sources upon the surface of the parabolic reflector, provided the plane of the image in the directrix is made independently luminous at every point to the degree illustrated by the curve of Fig. 4, and provided also the phase of the illumination at all points of the plane is the same. Equality of phase is essential because all points on the directrix are as distant from corresponding points on the parabolic surface as the focus is from those points.

In understanding the reflection of monochromatic light and of high frequency or short electromagnetic waves, the matter of the phase of the waves becomes very significant, but the determination of the phase in the case of the image of a source in an ideally perfect reflector is rather simple. In such a case, since a source and its image are at all times at equal distances from the reflecting surface, the phase of the image lags by the angle w behind that of the source, in which Z: is an odd integer. It is a fact that at any point on the perfectly reflecting surface, the motion of the resulting magnetic force due to the primary source and its image must be either zero or parallel to the surface.

Fig. 5 illustrates the operation of a parabolic reflector with a source of monochromatic light, or with an oscillator, preferably of constant frequency, at its focus. It is to be specially noted that the phase of the radiation from the image is constant throughout, its length being law behind that of the primary source at the focus of the reflector, 70 having I the integral value of 3 in the case assumed for illustration.

Clearly, when the primary source is a linear oscillator concentric with the focal line of the reflector, there is no need of transverse conductivity in the mirror, so that the metallic sheet of the continuous parabolic reflector of ill) thewell-known type may be replaced by the parabolic grid arrangements of wires or conductors parallel to the focal line of the reflector, as illustrated in Figs. 6 and 7. In

' the parabolic grid of Fig. 7, the wires or conductors are uniformly spaced, while n the parabolic grid of Fig. 6 they are so spaced that the density of their distribution in any area is proportional to the illumination which that area "wouldreceive from a source of light at the focus, or

ds given mathematically, as determined by Equatlon (3), glven heremabove. In passing from a continuous reflecting surface to' one formed of agrid or array of parallel ires or conductors, caution must be exercised lest the distance between the sending wires of the grid or array be insufficiently small relative to the wave length. The requisite distance between the grid or'array Will be considered in detail hereinafter. it must be borne in mind that the classical laws of reflection of light from a mirror surface, upon which is based the ordinary theory of a parabolic mirror, depend upon the. conboring points on the surface of the mirror.

However, in the case of a surface formed of parallel Wires or conductors, this interference can never be quite complete. Instead of complete neutralization,diffractive fringes are formed in addition to the main reflected beam, which, except for diifraction, follows the classical laws of reflection. As the wires or conductors are brought closer and closer, these-diffraction fringes become less important,-until there remains sensibly but a uniform reflected beam, as inthe case'of light reflected from a continuous reflecting surface. ltshould be remembered that the matter of radio differs widely'from the matter of light in that the dimensions of the radio reflector correspond to those of a microscopical- V ly small light mirror in which the phenomena of diffraction are of the utmost importance. For this reason, the light analogue, in spite of its great'simplicity and familiarity, will be used with utmost caution hereinafter as it is employed to aid in a better understanding of this invention.

In this invention, it'is proposed to employ the parabolic grids or arrays of Figs. 6 and 7 without any source of radiation at the focus. I

In the organization of Fig. 6, each Wire or conductor is made the seat of an alternating current of the same frequency and amplitude as any other wire or conductor, but the phase of the current in each wire or conductor is determined from Equation (2), given here inabove. In the organization of Fig. 7, the Wires or conductors are made the seats of alternating currents of the very same frequency, but both the amplitudes and the phases of these currents vary from wire to wire. The phase of the current is determined from Equation (2), given hereinabove, and the amplitude I (is is determined from Equation (8), also given hereinabove.

in any parabolic array, it is of the utmost importance to remember that the currents do not have the same initial phase, and, more over, that the currents donot have difierent frequencies. l Vhen an improper relationship is maintained between the various Wires or conductors. it is fatal to the production of a directive system, especially one of the *inhly eiiic-ient directive systems contemp ated in this invention.

In the ordinary parabolic mirror, which is employed in a well-known manner to secure a parallel. beam of light, none of the light from the primary source at the focus passes through the reflector to produce an illumination behind the reflector; yet, if the primary source of light at the focus be suppressed and the parallel beam be secured by making the mirror, itself, incandescent throughout its surface, a large portion of the total light developed'is radiated backwardly through the convex surface of the mirror. imilarly, in

radio, or rather in high frequency or short wave electromagnetic energy, a beam of radiation may be secured by setting up appropriate currents in the wires or conductors of the parabolic grid or array. However, half of the energy is radiatedbackwardly from the convex side of the array, as well as forwardly. The arrangement disclosed in. Fig. 8 is intended to obviate this diiliculty. in

the organization of this figure, a second and identical parabolic array is shown, for the purpose of illustration, ituated at a predetermined distance behind the first parabolic array. The distance between these parabolic arrays 1s o-nequarter of a wave length,

Currents identical as to amplitude and fre quency with those in the first array are set up in the second array, but the phases of the currents in the second array lead the corre sponding currents in the first array by a PI&5-

determined phase angle, one-quarter of a cycle 111 the case illustrated,

In this arrangement, any pair 01 corresponding conductors in the two arrays constitutes a. uni-direc onal couplet of having a. directional characteristic which acar dioid, shown in t) of the drawings. in this latter ligure, the reference characters 1 and E2 designate a corresponding pair of conductors in the first and second pa bolic arrays, respectively, and the cardioid is the polar curve representing its directional transmitting and receiving properties.

in the production of a pa allel beam of ight by means of a cylinr ical parabolic irror, has been pointed Ollb in connection h 2, which has an incandescent lilanient coaxial with the line of the focus, that the image of the li mine-us source appears to be a continuously 1 lm ed plane which is coincident with the plan f the directrix of the cylinorical parabola.

it has also been shown that in the absence or" the incandescent filament and oi the parabolic mirror, it possible to develop the same parallel beam of light by making the plane oi the image in the directrir; independently luminous throughout, provid 'l the real or actual l I i at every point equal to the trout in niinosity as an image of the incandesceni lil... cut at the focus.

it is similarly possible to secure the same 7 approximately parallel electromagnetic beam of radiation from a linear array of sources, such as is shown at the lower part of Fig. 6, as from the parabolic array of the figure, provided the currents throughout the linear array are all of equal magnitude and of the same'phase. The magnitude of the current common to all of these conductors is the same as the amplitude of the currents common to the conductors of the parabolic array, in order that the two beams may have the same, or substantially the same, absolute intensities at all points. Moreover, the same approximately parallel beam of radiation as that just considered may be secured by the employment of a horizontal array of oscillators or other sources shown at the lower part of Fig. 10, provided the currents in these oscillators are all of the same phase, and provided the amplitudes of these currents are proportional to the ordinates of the curve of Fig. 4. In general, whatever may be the distribution of the wires or conductors in-any linear array, or in any parabolic array, the distribution of the current amplitudes must be such as to provide a distribution of intensity in the beam, such as is shown in Fig. 2 of the drawings, and more explicitly given in Fig. l. In other words, the amplitude of a current in any wire of a parabolic array must be proportional to image array is determined'from the fact that it is the same as the amplitude of the current 111 the wlre of the parabolic array oi: which it is a projection on the directrix.

Radiation will take place backwardly as well as forwardly in the case of the image or linear rrays oi a single layer just as in the case'of the parabolic arrays of a single layer, with the result that there will be a loss of some of the advantages to be gained by making the system directive. However, this may be overcome by employing the arrangements illustrated in Figs. 11 and 12 of the drawings. The direction of the radiated beam in each of these cases is indicated by the arrow. A separation between the pairs of arrays is predetermined and taken each of one-quarter 01" a wave length, and consequently the applied currents in the front layer lag, by a quarter ofa cycle behind those in the rear layer, in order that these currents may be in phase and their eilects cumulative in the desired direction.

Although the cardioid directive characteristic of the couplet shown in Fig. 9 permits no radiation, or substantially negligible radiation, backwardly, i. e., in the direction 6 0, it nevertheless permits very considerable radiation in almost every other direction, particularly forwardly, i. e., in the direction 6 180". Yet, when greater efficiency of transmission and reception and greater directive exclusiveness are desired than are provided by the arrangements shown in Figs. 8, 11 and 12, in each of which a couplet of the type shown in Fig. 9 is employed, it is desirable to use two couplets which are so relatively spaced and phased as to restrict the radiation to an even narrower range in the general direction of the parallel beam which is intended to be transmitted or received.

A preferred form of the array produced by the combination of two couplets of the type shown in Fig. 9 is illustrated in Fig. 18. The reference characters A and A and A and A designate two pairs of conductors, the conductors of each pair being separated by apredetermined distance, such as one quarter of a wave length In this arrangement, the transmission takes place in the direction from A and A to A and A, and the phase of the currents impressed on the conductors A and A" lags by the angle J behind the phase of the currents impressed on the conductors A and A'. The polar curve (a) of Fig. 14' exhibits the directive characteristics of one of these couplets, such as A and A. However, A and A and A and A represent two pairs of conductors separated by a distance of, for example, onehalf wave length and the currents in each pair of conductors are of the same phase. The polar curve (6) of Fig. 14 exhibits the directive characteristics of the couplet such as A and A.

A couplet comprising two conductors, such as A and A may be regardedas a single conductor situated midway between A and A having a mean phase of, for example,

and having the directive characteristic (a) of Fig. 14. Yet, Fig. 13 comprises an array which may be regarded as a pair of such equivalent conductors. The directive characteristics of such a pair of equivalent conductors may be obtained from the product of the characteristics ofthe two types of couplets of which it is composed, and these directive characteristics are shown graphically by curve (a) of Fig. 1%. It will be understood that when a parabolic array or a parabolic image array is composed of directive couplets instead of simple radiating conductors, it becomes possible to usearrays having lateral widths less than those which would otherwise be possible, without at the same time suffering too great a diffractive spreading of the beam.

Fig. 15 illustrates a parabolic array based on the type shown in Fig. 13." Such an array may be employed to produce a narrow beam in which therewill be no radiation, or substantially no radiation, from the convex side 7 of the array. Fig. 16-illustrates a parabolic image array based on the type shown in Fig.13 for the production of a narrow beam in one directiononly. This arrangement is a modification ofthe linear or image arrays of Figs. 6 and 11. Fig. 17 illustrates another parabolic image array based on the type shownin Fig. 13, for the production'of a parallel beam in a single direction. This arrangement is a modification of the linear arrays of Figs. 11 and 12. From the foregoing disclosure, it will become apparent that one skilled in the art may properly construct a parabolic array or a parabolic image array that will produce an approximately parallel beam of radiation. The number of conductors or wires and their relative proximity will be considered in some detail hereinafter. V

The specific means by which currents in the radiated conductors are given their essential relative amplitudes and phases is in each case determined by different conditions. Figs; 18 and 19 illustrate how the length of the supply mains may be employed to secure the requisite relative phase variation between the currents in the radiating conductors of a parabolic array and a parabolic image array, respectively, the phases of the currents in F i 18 being different from one another and the phases of the currents in Fig. 19 being all alike. Figs. 20 and 21 of the drawings illustrate the use of, for example, what may be called lumped phase shifters in the supply mains to bring about the requisite phase variation. Throughout Figs. 18 to 21, inclusive, the reference character G designates a common energizing source, and the equal radiating conductors are made to sym bolize the equality of current amplitudes in these conductors. In Figs. 20 and 21, a num: ber of boxes are shown to which the reference characters 1, 92, (p3, etc., are attached, these boxes enclosing the lumped phase shifters mentioned hereinabove. Yet it will be understood that it is within the scope of this invention to employ any well-known phase developed herein have in each instance been described in connection with the development 7 of a beam of radiation, but it is clear that since the problems of directive transmission and of directive reception are conjugate problems, these arrays developed explicity. for transmission are implicitly also directive receivers. The common source G of alternat ing current in the radiating conductors of the transmitting arrays is connected to eachjof these conductors through a suitable phase shifter, as has been mentioned hereinabove."

Be this phase shifterlinear, as in Figs. 18

and 19, or lumped, as in Figs. 20 and 21, the

common receiving device of the receiving array-may nevertheless be connected toeach receiving wire or conductor of this array through some equally suitable phase shifter. These phase shifters may preferably be ident cal, Wire fer Wire, with those of the c me-- sponding transmitter. In other words, it is sufiicient to replace I the generator G by a suitable receiver or demodulator to convert the arrangement from the directive radiating system to the corresponding directive receiving system.

Precautions must be exercised in developing and constructing the various arrays in View of the effects of diffraction due to the relative smallness of the length of the arrays when measured in wave lengths, and moreover, due to the building up of arrays of discrete oscillators separated by some distance comparable with the wave length. These matters will be considered hereinafter.

Fig. 22 of the drawings shows a plurality of radiators or oscillators equidistant from one another, through which flow currents of equal magnitude and of the same phase. Let A and A be right sections through the equatorial plane of two equal oscillators separated by a distance (Z. Let these oscillators support equal oscillations, each of which may be given by the following expression:

I cos wt (5) in which a) is the periodicity. Consider lines drawn from a very distant point of observation in the equatorialplane making an angle \[1 with the line joining A and A; then the effect at the point of observation due to the current in oscillator A will be proportional to the following expression:

cos (mi cos -d (6) It is clear that the joint effect at the point of observation Wlll be proportional to the following expression:

cos cos 1/1) cos (wk- 4 (8) Another pairof oscillators Band B identical with oscillators A and A and supporting the same oscillations given by expression (5) are separated by the distance 3d. he effect of this pair of oscillators at the distant point of observation will be correspondingly proportional to'the following expression cos cos 1,0) cos (wt-(t) (9) Another and third pair of oscillators C and C identical with the first and second pairs and supporting identical oscillations are separated by a distance 5d. The effect of this pair of oscillators at the distant point of observation will be correspondingly pro-portional to the following expression:

i cos It will be obvious that if there be a linear array of 7r such equal pairs of equal oscillators supporting equal oscillations, and in which each oscillator is a distance d from its adjacos b) cos (wt-) (10) cent oscillator, the amplitude of the effect at the point of observation will be proportional to the following expression:

cos 11/) (1 2) in which m is odd; and the maximum amplitude, i. e., the amplitude at will be unity. Expression (12) is convenient for comparing the directive characteristics of arrays. It is to be noted, however, that the array of Fig. 22 is not a parabolic image array, but is an array which differs from the parabolic image array in that the intensity or current amplitude is uniform through out. Such an array will be referred to hereinafter as a uniform amplitude array. A study of this array will clearly bring out that the diffractive effect is dependent upon and is due'to the length of the array and to the relation of the interval (Z between oscillators to the wave length If the number of equal oscillators in an array of finite length Z be infinite and the amplitude of oscillations common thereto be infinitesimal, the array represented in Fig. 23 becomes in effect a continuous conducting sheet supporting auniform oscillatory current sheet in which the current per unit length of the sheet is given by the following equation:

i=A cos of (18) If ($72. is the effect at the distant point of observation in the equatorial plane due to the element clan of the current sheet, then the total 1,eos,eee

effect at the point of observation will be given by the following expression:

l h=A cos (wt cos yb dx (14) Equation (14), after integration, becomes wl h=AA (X cost) 15) 7r cos =11 For the sake of simplicity, it may be as sumed that Thereupon, the field strength may be determined from the following expression:

1 (l ,0 sn cos cos 1,0 But when 1/1 h vrl and therefore I sin cos 11/) i represents the directional characteristic. The array of Fig. 23 is in elfec-t the limiting case of the array of Fig. 22 which is reached 12: fl cos ,0

when (Z becomes infinitesimal and when 71' be-- comes infinite. Suchv an array will be referred to hereinafter as a continuous uniform amplitude array.

Fig. 24 shows in contrast the cartesian directive characteristics of continuous uniform amplitude arrays of different lengths, such, for example, as to 4A, inclusive. This figure shows, among other things, that the beam is very much'broadened by diffraction in the case of an array whose length is equal to the wave length. The beam becomes progressively narrower as the length of the array is increased, but fringes'appear and multiply, however, as the length of this array is increased.

Fig. 25 shows the Cartesian. characteristics of two uniform amplitude arrays as con',

of two and four oscillators is clearly shown, 1

but the absolute magnitude of this added orgreater diffraction is still more clearly shown 'ous parabolic image array are given 25, and the distances between the ordinates of,

curves (2) and (1) of the same figure. It is to be specially noted that the effect of the separation between the oscillators of the array is to enhance the diffraction which results in the case of the continuous array. The greater the separation, the greater the mag nification of the diffraction.

Fig. 27 shows the cartesian characteristics of two uniform amplitude arrays as contrasted with a continuous uniform amplitude array. A length common to the three arrays has been chosen merely for the purpose of illustration, to be two wave lengths, 2A. In this figure, the continuous line curve corresponds to the continuous array, while the curves (not drawn) indicated respectively by the triangles and crosses correspond to arrays of six and four oscillators, respectively. The added diffraction in the case of the arrays composed of discrete oscillators is again apparent, as is also its increase with the separation between the oscillators. The absolute magnitude of this effect is made much clearer in Fig. 28 of the drawing. curve (4)(1) is the enhanced difiraction in the case of four oscillators. Curve (3)(1) is the enhanced diffraction in the case of an array of six oscillators, and (2)(1) is the enhanced diffraction in the case of an array of eight oscillators. Curves (4)(1) and of Fig. 28 should be compared with curves (3)(1) and (2)(1) of Fig. 26, re-

spectively. Since in these corresponding.

curves the separation between the oscillators, expressed in wave lengths, is the same, it ap pears that the longer the array, expressed in wave lengths, the larger the separation between the oscillators, expressed in wave lengths, may be, though this permissible increase is not directly proportional to the increase in the length of the array. It is clear that the enhancement of the diffraction is already practically negligible, when the separa tion between the oscillators is as small as a quarter of the wave length, and that a greater separation may often be tolerated. However, thedegree of difiraction mayreadilybe determined from the information given herein, though the computation be somewhat tedious.

The directive characteristics of the continuous parabolic array and the continuous parabolic image array do not lend themselves as easily to direct analytical solutions as does the continuous constant amplitude array. By approximation, the characteristics of the continuous parabolic array and'the continuherein in Figs. 29 and 30. In Fig. 31, an approximately continuous In this figure,

its

parabolic image array of continuous uniform amplitude arrays is built up. In this figure, the continuous curve representsthe amplitude variation in a continuous parabolic image array having a predetermined length of, for example, 4).. The approximate parabolic image array abefijmnoplclghccl consists of the sum of the continuous uniform amplitude arrays abcd, @fgh, z'ji'cl, and mnop, which have, for example, the relative amplitudes of 0.3, 1.7, 1.9 and 1.1, respectively, and which have lengths l). to A, respectively.

The fringes exhibited by the curve of F 29 are due to tae echelon character of the array of Fig. 31. The directional characteristic of the corresponoing' uniform parabolic image array is given by the curve ABC having a discontinuity at B. It is this discontinuity which prevents a simple analytical solution forthe continuous parabolic image array.

Fig. 30 contrasts the polar directional characteristics of a continuous uniform amplitude array of, for example, three wave lengths, 3A with that of the continuous parabolic image array of, for example, four wave lengths, 4a. Though the principal beam of the shorter uniform amplitude array is a somewhat more nearly parallel beam than the beam of the parabolic image array, nevertheless the secondary beams or fringes of the uniform amplitude array militate somewhat against its usefulness. The parabolic image array and a corresponding parabolic array have the extraordinary property of radiating no energy, or negligible energy, beyond a certain critical angle, which in the array whose length 1s, for example, four wave lengths, 1s approximately 68. In other words, the broadening of the beam by diffraction is, in this case, limited to 22 on either side of the normal. It is due to the absence of diffraction fringes that parabolic'arrays and parabolic image arrays become of considerable importance.

Though the image adopted of exhibiting the efiects of diffraction, which is based upon computations of these effects in the case of uniform amplitude arrays, is undoubtedly the one best adapted to the purpose, nevertheless, in determining the characteristic of a given parabolic array, or its corresponding parabolic image array, when these are of the type illustrated in Fig. 10, itis best to use the speciiic series for these arrays, which is as follows:

If, on the other hand, the array be of the parabolic or image type, illustrated in Fig. 6, it is best to use the specific series for this type, which is as follows:

*- 0 cos 7 a tan I cos 1/) (19) These last two series are easily deduced by the same principles and in the same manner as Equation (12). When some other law of spacing the oscillators in a parabolic or imarray is used, the corresponding series can be easily determined by the principles and methods already disclosed, if the equation of the parabola is borne in mind and the steps given in connection with Equations (5)(12) be followed.

This invention has been described in some detail so as to aid in better understanding the complex phenomenaof this invention. It will be understood, however, that while this invention has been described in certain particular embodiments, merely for the purpose of illustration, the general principles of this invention may be applied to other and Widely varied organizations without departing from the spirit of the invention and the scope of the appended claims.

lVhat is claimed is 1. A directive antenna system comprising a linear array of parallel conductors which are equally spaced, said conductors being energized with currents of unequal and predetermined magnitudes and of the same phase.

2. A directive antenna system comprising a linear array of conductors, said conductors being placed side by side at equal intervals,

and means for energizingsaid conductors with currents of unequal and predetermined amplitudes and of equal phase and frequency, said array effecting a beam of energy equivalent to that of a cylindrical parabolic surface having an equivalent source of energy coincident with its focal line.

8. A directive antenna system comprising a plurality of pairs of linear arrays, each linear array consisting of a plurality of radiators of equal spacing, the linear arrays of each pair being separated by a predetermined distance, said pairs of arrays being side by side and at a definite distance from each other. H

4. The method of securing unidirectional transmission with a plurality of linear antenna arrays, which consists in grading the intensities of excitation along the conductors in any one linear array so that their cumula- 'tive directive effect shall approximate the directive effect of an equivalent parabolic array, and ad usting the phases of the currents 1n the conductors in any one row or column of the arrays in accordance with the distances between the conductors in that row or column.

In testimony whereof, I have signed my name to this specification this 12th day of 

